We study the clusterization of phase oscillators coupled with delay in complex networks. For the case of diffusive oscillators, we formulate the equations relating the topology of the network and the phases and frequencies of the oscillators (functional response). We solve them exactly in directed networks for the case of perfect synchronization. We also compare the reliability of the solution ...

Thetiming jitter in relaxation oscillators is analyzed. This jitter is described by a single normalized equation whose solution allows prediction of noise in practical oscillators. The theory is confirmed by measurements on practical oscillators and is used to develop a prototype low noise oscillator with a measured jitter of 1.5 ppm rms.

Analysis of non-laminar flows in coarse alluvial beds has a wide range of applications in various civil engineering, oil and gas, and geology problems. Darcy equation is not valid to analyze transient and turbulent flows, so non-linear equations should be applied. Non-linear equations are classified into power and binomial equations. Binomial equation is more accurate in a wide range of velocit...

A mathematical model for evoked potentials is outlined. The model has been developed by considering phase synchronisation of the underlying neurological processes. Tbe model, consisting of an ensemble of uncoupled linear oscillators with a gaussian distribution of frequencies is shown to reproduce tbe typical response of PIOO visual evoked response. Tbe model structure is parallel in form and i...

We present the non-Markovian generalization of the widely used stochastic Schrödinger equation. Our result allows to describe open quantum systems in terms of stochastic state vectors rather than density operators, without Markov approximation. Moreover, it unifies two recent independent attempts towards a stochastic description of non-Markovian open systems, based on path integrals on the one ...

– A unitary operator which relates the system of a particle in a linear potential with time-dependent parameters to that of a free particle, has been given. This operator, closely related to the one which is responsible for the existence of coherent states for a harmonic oscillator, is used to find a general wave packet described by an Airy function. The kernel (propagator) and a complete set o...

A system composed by interacting dynamical elements can be represented by a network, where the nodes represent the elements that constitute the system, and the links account for their interactions, which arise due to a variety of mechanisms, and which are often unknown. A popular method for inferring the system connectivity (i.e., the set of links among pairs of nodes) is by performing a statis...

In this work, we study the formal connections between non-linear Fokker-Planck Equation associated with non-additive entropy and Boltzmann correlation functional. The collisional term following $q$-algebra is adopted. derivation of Equation, two constraints are imposed on final result: i) that entropic index $q$ a characteristic parameter systems value does not change time, ii) for $q \rightarr...